Question

The question: A two port amplifier has been designed to match the
source and load resistances Rin = 1k ohms, Rout = 16 ohms, A =
50dB. What is the amplitude of the input signal needed to deliver
1W to the 16 ohm resistor?

Answer: 45.3 mV

My solution: I started by saying 1W = Vo^2 / R and Vo = 300Vin
because 50dB = 300 and then i solved for Vin using R=16 ohms....
what am I doing wrong?